I don't own VI, but through doing the news and paying attention to AARs and demogames out there, I am familiar with it enough I feel confident I could hold my own in a multiplayer game were I to join one tomorrow.  Personally, I have slipped back down to the don't even PLAN to purchase it unless it comes with pitboss/PBEM down the line, though. 

I would compare them to vanilla 4 and Civ 3.  Those were really quite similar when you boil them down, and you could just call it a graphical update. 

5 threw everything out the window.  6 feels a natural progression and refinement off of 5, much like 4 did off of 3. 

Graphically, I like 6 a lot better just because it's easier on my colorblindness.  The new cities and mapping concepts are the core of 6.  It's a big change in itself.  It's also meant to mask some of the worst issues with V by giving the players more choice, and thus more control. 

I think they've made more problems than they really solved, however, due to a completely inept AI that bleeds more the deeper people get into the game and start getting into the min/max gameplay.   They set out to make a game that forced you to adapt to your situation, and are ending up with one that is even more of a straight lined pre-programmed checklist than ever. 

Nothing patches/expansions can't fix, mind you.  Just in it's present state, it's pretty pointless IMO.